Question

In patrulaterul convex ABCD, m(B)=75 grade, iar masurile unghiurilor A,C,D sunt invers proportionale cu numerele: 0,1(6); 0,25; 0,1(1). Calculati masurile unghiurilor patrulaterului ABCD.

Answer 1

B=75°
A*0,1(6)=C*0,25=D*0,1(1).
A*1/6=C*1/4=D*1/9
A/6=C/4=D/9
4A=6C
C=4A/6; C=2A/3
9A=6D
D=9A/6; D=3A/2

A+B+C+D=360°

A+75+2A/3+3A/2=360°
6A+4A+9A=2160-450
19A=1710
A=1710:19
A=90°
C=2*90/3
C=60°
D=3*90/2
D=135°